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Probability Fundamentals: From Theory to Practice

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Learn how to calculate probabilities, differentiate between outcomes, and grasp the concept of mutually exclusive events. Enhance your knowledge of probability calculations through engaging examples and exercises.

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Probability Fundamentals: From Theory to Practice

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  1. Probability OCR Stage 6

  2. Probability • In an experiment, things that can happen are called possible outcomes • Each of these has a possibility

  3. Probability of an event happening • Probability = Required OutcomeTotal Possible Outcomes • i.e. The number of required outcomes divided by the total number of possible outcomes

  4. Getting a 4 on a single dice • There is 1 required outcome – a four • There are 6 possible outcomes • P(4) = 1 The answer may be written as a fraction, decimal or percentage 6 NEVER as “one out of six” The P says, “The probability of”

  5. The probability of not getting a 4? • There are five numbers on the single dice that are not a 4 • There are six possible outcomes • So, P(Not getting a 4) = 5 6

  6. The total probabilities of any event have a total of 1 1/6 + 5/6 = 1 It is important that you notice that the two probabilities add together to give 1 Probability of not getting a 4 on a single dice Probability of getting a 4 on a single dice

  7. Sum of all probabilities equal 1. Example The probability of a football team’s results in the next match are: • P(Win) = 0.3 • P(Lose) = 0.5 • What is the probability of a draw?

  8. Remember the total of all the probabilities is 1 The team must win, lose or draw. • P(Win) + P(Lose) + P(Draw) = 1 • 0.3 + 0.5 + P(Draw) = 1 • 0.8 + P(Draw) = 1 • P(Draw) = 0.2 This is 0.5 This is 0.3

  9. Mutually Exclusive events • Can NOT happen at the same time • Examples • A HEAD and a TAIL when coin is spun • A 6 and an odd number when die rolled • A level 5 and a level 6 on a SAT paper

  10. Example • Sam and Pete play chess • P(Sam wins) = 0.4 • P(Pete wins) = 0.3 • What is P(Draw) ? • 0.4 + 0.3 + P(Draw) = 1 • 0.7 + P(Draw) = 1 • P(Draw) = 0.3

  11. Exercises – to be completed next lesson • OCR Stage 5/6 Text, • Stage 6, Chapter 4, Page 182 • Ex 4.1A • Ex 4.1B • Ex 4.2A • Ex 4.2B

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